Tunable Contact Types and Interfacial Electronic Properties in TaS2/MoS2 and TaS2/WSe2 Heterostructures

Following the successful experimental synthesis of single-layer metallic 1T-TaS2 and semiconducting 2H-MoS2, 2H-WSe2, we perform a first-principles study to investigate the electronic and interfacial features of metal/semiconductor 1T-TaS2/2H-MoS2 and 1T-TaS2/2H-WSe2 van der Waals heterostructures (vdWHs) contact. We show that 1T-TaS2/2H-MoS2 and 1T-TaS2/2H-WSe2 form n-type Schottky contact (n-ShC type) and p-type Schottky contact (p-ShC type) with ultralow Schottky barrier height (SBH), respectively. This indicates that 1T-TaS2 can be considered as an effective metal contact with high charge injection efficiency for 2H-MoS2, 2H-WSe2 semiconductors. In addition, the electronic structure and interfacial properties of 1T-TaS2/2H-MoS2 and 1T-TaS2/2H-WSe2 van der Waals heterostructures can be transformed from n-type to p-type Schottky contact through the effect of layer spacing and the electric field. At the same time, the transition from Schottky contact to Ohmic contact can also occur by relying on the electric field and different interlayer spacing. Our results may provide a new approach for photoelectric application design based on metal/semiconductor 1T-TaS2/2H-MoS2 and 1T-TaS2/2H-WSe2 van der Waals heterostructures.


Introduction
Due to their remarkable material properties and enormous potential for use in a wide variety of technological device applications, novel 2D materials have attracted a significant amount of attention from researchers. Graphene [1,2] as the first material to promote the field of 2D materials research has many remarkable properties, such as massless Dirac fermions [3], high carrier mobility [4], high conductivity [5], and an unconventional quantum Hall effect at room temperature [6]. However, high-speed electrical applications like field-effect transistors are limited by the lack of a bandgap in graphene [7]. Therefore, the research community has been actively searching for 2D semiconductor materials with excellent properties and applications. In recent years, TMDs, a whole new class of 2D materials, have been studied as the most attractive materials due to their excellent properties. Because of their inherent advantages, such as a high surface-to-volume ratio, no dangling bonds, and excellent carrier mobility, TMDs [8][9][10][11] are important technical materials for various energy, electronic, and optoelectronic applications in the future.
Among TMDs, 2H-MoS 2 and 2H-WSe 2 , the two most typical TMDs materials, have fascinating properties and a wide range of applications. The bulk structure of MoS 2 is stratified, with weak van der Waals (vdW) forces between layers. Unlike graphene, monolayer MoS 2 is a direct bandgap [7,8] semiconductor with a bandgap of 1.8 eV. Moreover, single-layer MoS 2 has a high on/off current ratio of about 10 8 and a high carrier mobility [9] of 200 cm 2 /V −1 s −1 at room temperature, making it promising in field-effect transistors [7] (FETs), photodetectors [10], and electroluminescent devices, thus demonstrating its considerable application potential. So far, the structural, mechanical, electronic, and transport properties of MoS 2 monolayers have been extensively studied, both experimentally and theoretically [11][12][13][14][15][16][17]. The results show that the physical properties of MoS 2 monomolecular film are very sensitive to external conditions, such as the strain and electric field. Furthermore, 2D WSe 2 is an indirect bandgap semiconductor with a rather large bandgap.
In the past few years, the electronic properties, thermoelectric response [18], and strain engineering [11,[19][20][21] of WSe 2 have been extensively studied. At the same time, important applications of WSe 2 in transistors [22][23][24], phototransistors [25], circuits [26,27], and magnesium-ion batteries [28] have also been discussed. Furthermore, single-layer and fewlayer WSe 2 have been experimentally synthesized [29][30][31], which makes the fabrication of high-performance WSe 2 -based nanoelectronics devices promising. Different from 2D MoS 2 and WSe 2 monolayers, we note that 1T-TaS 2 , as an emerging 2D layered TMD, is one of the most studied TMDs due to its unexpected physical properties. The structure of 1T-TaS 2 is similar to the 2H phase of MoS 2 , but it exhibits different metallic properties [32,33], so it is very important for our next research work.
The electrical contacts between metals and semiconductors are frequently used in modern electronic and optoelectronic devices, which can not only greatly improve the charge injection efficiency of semiconductors, but also improve the performance of electronic devices. The study of metal/semiconductor interfacial contacts is a crucial step in the construction of energy-efficient and high-performance electronic devices. The functionality of the device may be compromised partially or totally in the event of inappropriate contact between the metal and the semiconductor. Therefore, the formation of a low or eliminated Schottky barrier height (SBH) [22,34] in the metal-semiconductor junction (MSJ) from the Schottky to the ohmic contact is critical for the fabrication of high-performance nanodevices. Since most 2D metal-semiconductor interfaces are essentially Schottky interfaces [35,36], there will be intrinsic and extrinsic limitations, including surface defects, work function mismatch, and sustainable doping strategies; thus, Schottky Converting base contact to ohmic contact is indeed a challenging task.
The high contact resistance [37] of transition metal dichalcogenide (TMDs) devices is one of the bottlenecks limiting the application of TMDs in various fields. The contact [38] resistance of TMD-based devices is closely related to the contacted metal/TMDs interface and band alignment [39]. So far, a large number of theoretical experiments [40] have demonstrated that the vdW interaction can generate good contact properties in metaltransition metals [41,42] and semimetals-transition metals [43]. Therefore, vdW contacts have a very wide range of applications.
To date, the tunable Schottky barrier and electronic properties of the 1T-TaS 2 /2H-MoS 2 (2H-WSe 2 ) combination have not yet been investigated. Based on this idea, we constructed 1T-TaS 2 , 2H-MoS 2 (2H-WSe 2 ) monolayer structures, respectively. In this work, we performed first-principles calculations to investigate the atomic and electronic structures of 1T-TaS 2 /2H-MoS 2 (2H-WSe 2 ) vdWHs and their tunable electronic structures under interlayer spacing and the electric field. The vdW interaction between metallic 1T-TaS 2 and semiconducting 2H-MoS 2 (2H-WSe 2 ) monolayers makes the heterostructure energetically feasible and preserves the intrinsic properties of the two constituent monolayers. Our results predict that 1T-TaS 2 /2H-MoS 2 (2H-WSe 2 ) vdWHs have a tunable Schottky barrier height (SBH), and that the electronic structure and interfacial properties of 1T-TaS 2 /2H-MoS 2 (2H-WSe 2 ) vdWHs can be transformed from n-type to p-type ShC through the effect of layer spacing and the electric field. At the same time, the transition from ShC to OhC can also occur by relying on the electric field and different interlayer spacing. Our results reveal the potential role of metallic 1T-TaS 2 as an effective metal contact to semiconductor 2H-MoS 2 (2H-WSe 2 ).

Geometric Structures and Electronic Properties
In Figure 1, we showed the atomic structure, phonon spectrum, projected band structure, and state density of metallic 1T-TaS 2 and semiconducting 2H-MoS 2 , 2H-WSe 2 monolayer. After geometric optimization, the monolayers 1T-TaS 2 , 2H-MoS 2 , and 2H-WSe 2 all show layered atomic structures, and their lattice constants are 3.186 Å, 3.184 Å, and 3.184 Å, respectively, which is consistent with previous experimental and theoretical measurements. In Figure 1a-c, it can be seen that the Ta atom in metal TaS 2 is sandwiched between two S atoms, while the Mo atom and W atom are sandwiched between two S atoms and two Se atoms in semiconductor MoS 2 and WSe 2 monolayers, respectively. In addition, the 1T-TaS 2 layer in Figure 1g shows metallic behavior, while the 2H-MoS 2 and 2H-WSe 2 monolayers in Figure 1h, ishow semiconductor characteristics. 2H-MoS 2 shows a direct bandgap semiconductor while 2H-WSe 2 shows an indirect bandgap semiconductor. The bandgap values calculated by HSE06 are 2.32 eV and 1.97 eV, and those calculated by PBE are 1.66 eV and 1.46 eV, respectively. The results show that they are close to the experimental measurements [11] of 1.80 eV and 1.65 eV, which confirms the reliability of our calculation. In general, traditional PBE methods often underestimate the bandgap of 2D semiconductors, and HSE06 can be used to predict more accurate bandgap values. However, the PBE bandgap of the 2H-MoS 2 and 2H-WSe 2 monolayers is closer to the experimental bandgap than the HSE06 method. Therefore, we use the PBE method for all of the following calculations. Moreover, in Figure 1h,i, it is found that, in both PBE and HSE06 functional, the CBM and VBM of 2H-MoS 2 monolayer are located at the K point, while the CBM and VBM of 2H-WSe 2 monolayer are not at the same high-symmetry path. In addition, the state density of 1T-TaS 2 is shown in Figure 1g. For metal 1T-TaS 2 , the major contribution is the d orbital of Ta. Meanwhile, for the 2H-MoS 2 monolayer, the CBM is dominated by the d orbital contribution of Mo, and the VBM is dominated by the p orbital contribution of S. For the 2H-WSe 2 monolayer, the CBM is dominated by the d orbital contribution of W, and the VBM is dominated by the p orbital contribution of Se. The phonon spectrum of 1T-TaS 2 ,2H-MoS 2 and 2H-WSe 2 are reflected in Figure 1d-f. It can be seen that the frequencies of the three considered monolayers are all positive, and there is no negative frequency at the Γ point, thus confirming their dynamic stability.

Geometric Structures and Electronic Properties
In Figure 1, we showed the atomic structure, phonon spectrum, projected band structure, and state density of metallic 1T-TaS2 and semiconducting 2H-MoS2, 2H-WSe2 monolayer. After geometric optimization, the monolayers 1T-TaS2, 2H-MoS2, and 2H-WSe2 all show layered atomic structures, and their lattice constants are 3.186 Å, 3.184 Å, and 3.184 Å, respectively, which is consistent with previous experimental and theoretical measurements. In Figure 1a-c, it can be seen that the Ta atom in metal TaS2 is sandwiched between two S atoms, while the Mo atom and W atom are sandwiched between two S atoms and two Se atoms in semiconductor MoS2 and WSe2 monolayers, respectively. In addition, the 1T-TaS2 layer in Figure 1g shows metallic behavior, while the 2H-MoS2 and 2H-WSe2 monolayers in Figure 1h, ishow semiconductor characteristics. 2H-MoS2 shows a direct bandgap semiconductor while 2H-WSe2 shows an indirect bandgap semiconductor. The bandgap values calculated by HSE06 are 2.32 eV and 1.97 eV, and those calculated by PBE are 1.66 eV and 1.46 eV, respectively. The results show that they are close to the experimental measurements [11] of 1.80 eV and 1.65 eV, which confirms the reliability of our calculation. In general, traditional PBE methods often underestimate the bandgap of 2D semiconductors, and HSE06 can be used to predict more accurate bandgap values. However, the PBE bandgap of the 2H-MoS2 and 2H-WSe2 monolayers is closer to the experimental bandgap than the HSE06 method. Therefore, we use the PBE method for all of the following calculations. Moreover, in Figure 1h,i, it is found that, in both PBE and HSE06 functional, the CBM and VBM of 2H-MoS2 monolayer are located at the K point, while the CBM and VBM of 2H-WSe2 monolayer are not at the same high-symmetry path. In addition, the state density of 1T-TaS2 is shown in Figure 1g. For metal 1T-TaS2, the major contribution is the d orbital of Ta. Meanwhile, for the 2H-MoS2 monolayer, the CBM is dominated by the d orbital contribution of Mo, and the VBM is dominated by the p orbital contribution of S. For the 2H-WSe2 monolayer, the CBM is dominated by the d orbital contribution of W, and the VBM is dominated by the p orbital contribution of Se. The phonon spectrum of 1T-TaS2,2H-MoS2 and 2H-WSe2 are reflected in Figure 1d-f. It can be seen that the frequencies of the three considered monolayers are all positive, and there is no negative frequency at the Γ point, thus confirming their dynamic stability. 2H -WSe 2 , respectively. The brown, yellow, purple, silver, and green balls represent tantalum, sulfur, molybdenum, tungsten, and selenium atoms, respectively.

Structures and Electronic Properties of Heterostructures
We constructed vdWHs by stacking the monolayers 2H-MoS 2 and 2H-WSe 2 in the 1T-TaS 2 monolayer along the z direction and setting the initial equilibrium layer spacing D as 3.02 Å and 2.98 Å, which are greater than the sum of the covalent radii between Mo and S atoms and W and Se atoms, respectively. This confirmed that no covalent bond has been formed between the two constituent monolayers. It is clear that these calculated interlayer distances are comparable to other previously reported interlayer distances in vdWHs, including graphene/MoS 2 [44] and graphene/WSe 2 [45], which are typical vdW interactions. This finding shows that there are no chemical bonds in the 1T-TaS 2 /2H-MoS 2 (2H-WSe 2 ) vdWHs (in the following, the TaS 2 /MoS 2 (WSe 2 ) vdWHs stand for the 1T-TaS 2 /2H-MoS 2 (2H-WSe 2 ) vdWHs). At the same time, we consider the possible stacking configurations that form these two heterogeneous structures, corresponding to (a) and (b) in Figure 2, respectively. According to the calculation results, the energy of the first diagram on the left of the two vdWHs' stacking configurations is the lowest, and the Eb is −45.95920 eV and −45.86945 eV, respectively. Therefore, we used this stacking method to construct unit cells from (1 × 1) TaS 2 and (1 × 1) MoS 2 , (1 × 1) TaS 2 and (1 × 1) WSe 2 cells, respectively. According to the formula: m − n/m + n < 5% (m, n are the lattice constants of TaS 2 and MoS 2 (WSe 2 ), respectively), the calculated lattice constants of TaS 2 /MoS 2 , TaS 2 /WSe 2 vdWHs are both 3.18674 Å, and the lattice mismatch rate is 0.04%. Figure 1. (a−c) show the optimized atomic structure (top view and side view), (d−f) phonon disper-sion curve, (g−i) HSE06 projected band structures and state density of 1T-TaS2, 2H-MoS2, 2H -WSe2, respectively. (j−l) PBE projected band structures and state density of 1T-TaS2, 2H-MoS2, 2H -WSe2, respectively. The brown, yellow, purple, silver, and green balls represent tantalum, sulfur, molybdenum, tungsten, and selenium atoms, respectively.

Structures and Electronic Properties of Heterostructures
We constructed vdWHs by stacking the monolayers 2H-MoS2 and 2H-WSe2 in the 1T-TaS2 monolayer along the z direction and setting the initial equilibrium layer spacing D as 3.02 Å and 2.98 Å, which are greater than the sum of the covalent radii between Mo and S atoms and W and Se atoms, respectively. This confirmed that no covalent bond has been formed between the two constituent monolayers. It is clear that these calculated interlayer distances are comparable to other previously reported interlayer distances in vdWHs, including graphene/MoS2 [44] and graphene/WSe2 [45], which are typical vdW interactions. This finding shows that there are no chemical bonds in the 1T-TaS2/2H-MoS2(2H-WSe2) vdWHs (in the following, the TaS2/MoS2(WSe2) vdWHs stand for the 1T-TaS2/2H-MoS2(2H-WSe2) vdWHs). At the same time, we consider the possible stacking configurations that form these two heterogeneous structures, corresponding to (a) and (b) in Figure  2, respectively. According to the calculation results, the energy of the first diagram on the left of the two vdWHs' stacking configurations is the lowest, and the Eb is -45.95920 eV and −45.86945 eV, respectively. Therefore, we used this stacking method to construct unit cells from (1 × 1) TaS2 and (1 × 1) MoS2, (1 × 1) TaS2 and (1 × 1) WSe2 cells, respectively. According to the formula: m − n/m + n < 5% (m, n are the lattice constants of TaS2 and MoS2(WSe2), respectively), the calculated lattice constants of TaS2/MoS2, TaS2/WSe2 vdWHs are both 3.18674 Å, and the lattice mismatch rate is 0.04%. Furthermore, to verify the stability of the structure, the binding energy was calculated as , and E MoS2 (E WSe2 ) represent the total energy of the corresponding vdWHs, TaS 2 , and MoS 2 (WSe 2 ) monolayers, respectively. The binding energies of TaS 2 /MoS 2 (WSe 2 ) were −0.28 eV and −0.32 eV, respectively. The minus sign ("−" symbol) in the binding energy indicates that these vdWHs are energy stable. To evaluate the mechanical stability, we also calculated the elastic constant of TaS 2 /MoS 2 (WSe 2 ) vdWHs. The elastic constants C 11 , C 12 , and C 66 = (C 11 − C 12 )/2 of TaS 2 /MoS 2 vdWHs were calculated as 254 N/m, 63 N/m, and 95 N/m, respectively. Meanwhile, the elastic constants C11, C12, and C 66 = (C 11 -C 12 )/2 of TaS 2 /Wse 2 were calculated as 294 N/m, 45 N/m, and 124 N/m, respectively. It can be found that the elastic constants C11 > C12 and C66 > 0 of vdWHs satisfy the Born-Huang criterion [46,47], indicating that vdWHs are stable. In addition, we calculate Young's modulus and Poisson's ratio of Y = (C 11 2 − C 12 2 )/C 11 , V = C 12/ C 11 and other systems. The polar graphs of Young's modulus and Poisson's ratio of vdWHs are described in Figure S1, supporting the information. The average Young's modulus of TaS 2 /MoS 2 vdWHs is 238 N/m and the average Poisson's ratio is 0.25, while the average Young's modulus of TaS 2 /WSe 2 vdWHs is 287 N/m and the average Poisson's ratio is 0.15, which are lower than graphene54. It was shown that two vdWHs are susceptible to strain regulation.
The band structure of TaS 2 /MoS 2 , TaS 2 /WSe 2 vdWHs is shown in Figure 3. TaS 2 and MoS 2 (WSe 2 ) maintain their intrinsic band structure while forming heterostructures. The metal properties of the TaS 2 monolayer and semiconductor properties of the MoS 2 (WSe 2 ) monolayer are well preserved. In metal/semiconductor contacts, it is important to determine whether ShC or OhC contacts [48] are formed, reducing the Schottky barrier and improving charge injection efficiency. The weight band structure in Figure 3a,b showed that TaS 2 /MoS 2 and TaS 2 /WSe 2 vdWHs all formed Schottky contacts, and we found that the bandgap values of PBE were 1.58/1.63eV, respectively. It is well known that the Schottky barrier heights (SBH) of the n-type and p-type are determined by the Schottky-Mott rule [49] as Φ Bn = E CBM − E F and Φ Bp = E F − E VBM , where the conduction band minimum (CBM), valence band maximum value (VBM), and Fermi level are defined by E CBM , E VBM, and E F , respectively. In addition, to confirm the formation of the Schottky contacts in such heterostructures [48], we further plot the work functions of metallic TaS 2 , semiconducting MoS 2 (WSe 2 ) monolayers, and their corresponding vdWHs, as displayed in Figure 4a,b. The n-ShC SBH of TaS 2 /MoS 2 vdWHs was 0.5 eV, and the p-ShC SBH of TaS 2 /WSe 2 vdWHs was 0.49 eV. Notably, the SBH of TaS 2 /MoS 2 (WSe 2 ) vdWHs is very small, indicating that the MoS 2 (WSe 2 ) material can be considered an efficient 2D metal contact with the TaS 2 material.    The charge density difference in TaS2/MoS2(WSe2) vdWHs is shown in Figure 5a,b. In order to further understand the charge distribution in TaS2/MoS2(WSe2) vdWHs, the electron density difference is calculated as follows [50,51]: Δρ = ρvdWHs − ρTaS2 − ρMoS2(ρWSe2). Here, ρvdWHs, ρTaS2, and ρMoS2 (ρWSe2) represent the TaS2/MoS2(WSe2) combination vdWHs charge density and isolated TaS2 and MoS2(WSe2) monolayers, respectively.
The yellow area represents charge accumulation, whereas the cyan area represents charge depletion. Figure 5a,b clearly show that charge transfer occurs at the contact interface. For Figure 5a, the charge distribution is mainly concentrated at the contact interface between TaS2 and MoS2, where electrons are consumed in the Ta-S layer and accumulated in the Mo-S layer. As shown in Figure 5b, the charge distribution was mainly concentrated at the contact interface of TaS2 and WSe2, with electrons consumed on the W-Se layer and accumulated on the Ta-S layer. Therefore, the results indicate that the TaS2 and MoS2(WSe2) layers in the corresponding vdWHs exhibit weak interlayer interactions. The charge density difference in TaS 2 /MoS 2 (WSe 2 ) vdWHs is shown in Figure 5a,b. In order to further understand the charge distribution in TaS 2 /MoS 2 (WSe 2 ) vdWHs, the electron density difference is calculated as follows [50,51] Here, ρ vdWHs , ρ TaS2 , and ρ MoS2 ( ρWSe2 ) represent the TaS 2 /MoS 2 (WSe 2 ) combination vdWHs charge density and isolated TaS 2 and MoS 2 (WSe 2 ) monolayers, respectively. Figure 5c,d illustrate the mean in-plane average electrostatic potential of TaS2/MoS2(WSe2) vdWHs, respectively. Since the potential of TaS2 is higher than that of 2D MoS2, and the potential of 2D WSe2 is higher than that of TaS2, it indicates that the charge is transferred from the Ta-S layer to the Mo-S layer, and from the W-Se layer to the Ta-S layer, which is consistent with Figure 5a,b, which show that the direction of charge transfer is consistent. It can be seen that the interfacial charge transfer leads to the existence of a built-in electric field. Therefore, carrier mobility and charge injection may be affected. In addition, in order to prove that TaS2/MoS2(WSe2) vdWHs is suitable for high-performance nanodevices, it is essential to examine the carrier mobility of vdWHs. Therefore, carrier mobility and charge injection may be affected. In addition, in order to prove that TaS2/MoS2(WSe2) vdWHs are suitable for high-performance nanodevices, it is essential to The yellow area represents charge accumulation, whereas the cyan area represents charge depletion. Figure 5a,b clearly show that charge transfer occurs at the contact interface. For Figure 5a, the charge distribution is mainly concentrated at the contact interface between TaS 2 and MoS 2 , where electrons are consumed in the Ta-S layer and accumulated in the Mo-S layer. As shown in Figure 5b, the charge distribution was mainly concentrated at the contact interface of TaS 2 and WSe 2 , with electrons consumed on the W-Se layer and accumulated on the Ta-S layer. Therefore, the results indicate that the TaS 2 and MoS 2 (WSe 2 ) layers in the corresponding vdWHs exhibit weak interlayer interactions. Figure 5c,d illustrate the mean in-plane average electrostatic potential of TaS 2 /MoS 2 (WSe 2 ) vdWHs, respectively. Since the potential of TaS 2 is higher than that of 2D MoS 2 , and the potential of 2D WSe 2 is higher than that of TaS 2 , it indicates that the charge is transferred from the Ta-S layer to the Mo-S layer, and from the W-Se layer to the Ta-S layer, which is consistent with Figure 5a,b, which show that the direction of charge transfer is consistent. It can be seen that the interfacial charge transfer leads to the existence of a built-in electric field. Therefore, carrier mobility and charge injection may be affected. In addition, in order to prove that TaS 2 /MoS 2 (WSe 2 ) vdWHs is suitable for high-performance nanodevices, it is essential to examine the carrier mobility of vdWHs. Therefore, carrier mobility and charge injection may be affected. In addition, in order to prove that TaS 2 /MoS 2 (WSe 2 ) vdWHs are suitable for high-performance nanodevices, it is essential to examine the carrier mobility of vdWHs. For 2D systems, carrier mobility is closely related to effective mass because µ = eτ/m*. Thus, we established the effective masses of electrons (m e *) and holes (m h *) by fitting the band-edge dispersion VBM and CBM as follows: Here,h is Planck's constant and k is the wave vector. Our calculated m e * and m h * of TaS 2 /MoS 2 (WSe 2 ) vdWHs are listed in Table 1. The effective mass values that can find these electrons and holes are very small, which proves that TaS 2 /MoS 2 (WSe 2 ) vdWHs have a high carrier mobility. Therefore, they can be potential candidates for high-speed nanodevice applications.

Heterostructures under Interlayer Distance
It is well known that applying mechanical strain to change interlayer coupling can adjust the interface properties of heterostructures. Controllable SBH and contact types in TaS 2 /MoS 2 (WSe 2 ) vdWHs are one of the most important challenges to improve the performance of nanodevices. Therefore, we further investigate the effect of strain engineering by adjusting the interlayer distance and applied electric field. Furthermore, it is worth noting that the interlayer distance in 2D-based vdWHs can be controlled by scanning tunneling microscopy [52] or vacuum thermal annealing [53]. Here, the strain is applied by adjusting the layer spacing, defined as ∆D = D − D 0 , where the original D of MoS 2 and WSe 2 is 3.0 Å and 2.9 Å, respectively, and D 0 is the layer spacing after the strain. The tensile strain is defined by increasing the interlayer distance D, while the compressive strain is defined by decreasing D. ∆D < 0 represents the compressive strain, while ∆D > 0 represents the tensile strain. As shown in Figure 6a,b, for TaS 2 /MoS 2 vdWHs, it is found that the tensile strain tends to increase Φ Bn and decrease Φ Bp . In the case of ∆D > 0, the CBM of the MoS 2 layer moves upward away from the Fermi level, resulting in the increase in Φ Bn . On the other hand, VBM moves upward towards the Fermi level, resulting in a decrease in Φ Bp . TaS 2 /MoS 2 vdWHs changes with the SBH of ∆D, as shown in Figure 6c. When 0 < ∆D < 1 Å tensile strain, it can be seen that Φ Bp > Φ Bn . In this case, TaS 2 /MoS 2 has the n-ShC type. Moreover, TaS 2 /MoS 2 still maintains the n-ShC type under −0.8 < ∆D < 0 Å compression strain. However, when ∆D ≤ −0.8 Å, it is observed in Figure 6c that Φ Bn is gradually larger than Φ Bp , resulting in a transition from the n-ShC type to p-ShC type. Therefore, the SBH and contact types in TaS 2 /MoS 2 vdWHs can be adjusted by changing the layer spacing. On the contrary, As shown in Figure 7a,b, for TaS 2 /WSe 2 vdWHs, when ∆D is greater than −0.8 Å and less than 1.2 Å, according to the overall trend, we find that the WSe 2 layer of the CBM moves upward away from the Fermi energy level, resulting in an increase in Φ Bn . On the other hand, the VBM moves upward towards the Fermi level, resulting in a decrease in Φ Bp . TaS 2 /WSe 2 vdWHs changes with the SBH of ∆D, as shown in Figure 7c. It was observed that the SBH of TaS 2 /WSe 2 vdWHs varied linearly with layer distance. When 0 < ∆D ≤ 1.2 Å tensile strain, it can be seen that Φ Bn > Φ Bp . In this case, TaS 2 /WSe 2 has a p-ShC type. In addition, when −0.8 ≤ ∆D < 0 Å compressive strain, Φ Bn is still larger than Φ Bp . In this case, it indicates that TaS 2 /WSe 2 still maintains the p-ShC type. Therefore, the SBH in TaS 2 /WSe 2 vdWHs can be adjusted by changing the layer spacing, but the contact type cannot be adjusted.

Heterostructures under Electric Field
Furthermore, we considered the effect of the electric field on the electronic properties and contact types of TaS2/MoS2 (WSe2) vdWHs, as shown in Figures 8 and 9. It can be observed that the SBH of TaS2/MoS2 (WSe2) vdWHs changes linearly with the electric field. Here, the applied electric field is applied in the z direction of vdWHs. As shown in Figure

Heterostructures under Electric Field
Furthermore, we considered the effect of the electric field on the electronic properties and contact types of TaS2/MoS2 (WSe2) vdWHs, as shown in Figures 8 and 9. It can be observed that the SBH of TaS2/MoS2 (WSe2) vdWHs changes linearly with the electric field. Here, the applied electric field is applied in the z direction of vdWHs. As shown in Figure  8a,b, for TaS2/MoS2 vdWHs, by applying a positive electric field, the CBM of the MoS2

Heterostructures under Electric Field
Furthermore, we considered the effect of the electric field on the electronic properties and contact types of TaS 2 /MoS 2 (WSe 2 ) vdWHs, as shown in Figures 8 and 9. It can be observed that the SBH of TaS 2 /MoS 2 (WSe 2 ) vdWHs changes linearly with the electric field. Here, the applied electric field is applied in the z direction of vdWHs. As shown in Figure 8a,b, for TaS 2 /MoS 2 vdWHs, by applying a positive electric field, the CBM of the MoS 2 layer moves down to the Fermi level, resulting in a decrease in Φ Bn . Instead, VBM moves downward away from the Fermi level, causing Φ Bp to increase. Interestingly, changes in SBH and contact types can be seen in Figure 8c. When a positive electric field of 0 < E < 0.3 V/Å is applied, it can be seen that Φ Bp > Φ Bn . In this case, the n-ShC type exists for 1T-TaS 2 /2H-MoS 2 vdWHs. Surprisingly, when a positive electric field of E ≥ 0.3 V/Å is applied, it is found that the CBM of MoS 2 moves down through the Fermi level and can form a transition from the n-ShC type to n-OhC type in TaS 2 /MoS 2 vdWHs. Similarly, when a negative electric field of −0.14 < E ≤ 0 Å is applied, it can be found that Φ Bp > Φ Bn . In this case, the n-ShC type still exists for TaS 2 /MoS 2 vdWHs. However, when a negative electric field of −0.6 < E ≤ −0.14 Å is applied, it can be observed that Φ Bn is gradually larger than Φ Bp , indicating that TaS 2 /MoS 2 vdWHs can form a transition from the n-ShC type to p-ShC type. In addition, when a negative electric field of E ≤ −0.6 V/Å is applied, it can be found from the figure that the VBM of MoS 2 moves upward through the Fermi level, forming a transition from the p-ShC type to p-OhC type. Similarly, as shown in Figure 9a,b, for TaS 2 /WSe 2 vdWHs, the CBM of the WSe 2 layer moves upward away from the Fermi level by applying a positive electric field, resulting in an increase in Φ Bn . In contrast, VBM moves upward towards the Fermi level, resulting in a decrease in Φ Bp .
Molecules 2023, 28, x FOR PEER REVIEW 10 of 14 field of −0.6 < E ≤ −0.14 Å is applied, it can be observed that ΦBn is gradually larger than ΦBp, indicating that TaS2/MoS2 vdWHs can form a transition from the n-ShC type to p-ShC type. In addition, when a negative electric field of E ≤ −0.6 V/Å is applied, it can be found from the figure that the VBM of MoS2 moves upward through the Fermi level, forming a transition from the p-ShC type to p-OhC type. Similarly, as shown in Figure 9a,b, for TaS2/WSe2 vdWHs, the CBM of the WSe2 layer moves upward away from the Fermi level by applying a positive electric field, resulting in an increase in ΦBn. In contrast, VBM moves upward towards the Fermi level, resulting in a decrease in ΦBp.   Interestingly, changes in SBH and contact types can be seen in Figure 9c. When a positive electric field of 0 < E < 0.2 Å is applied, it can be seen that Φ Bn > Φ Bp . In this case, TaS 2 /WSe 2 vdWHs will form the p-ShC type. Shockingly, when a positive electric field of E ≥ 0.2 Å was applied, the VBM of WSe 2 was found to move upward through the Fermi level, forming a transition from the p-ShC type to p-OhC type. Furthermore, when a negative electric field −0.2 < E ≤ 0 Å is applied, it can be found that Φ Bn > Φ Bp . In this case, there is the p-ShC type in TaS 2 /WSe 2 vdWHs. However, when a negative electric field of −0.4 < E ≤ −0.2 Å is applied, it can be found that Φ Bp > Φ Bn can form a transition from the p-ShC type to p-OhC type. Moreover, when a negative electric field of E ≤ −0.4 Å is applied, the CBM of WSe 2 can be found to move down through the Fermi level, resulting in a transition from the n-ShC type to n-OhC type in TaS 2 /WSe 2 vdWHs. All the above results indicate that the application of an electric field can regulate the contact type and SBH of TaS 2 /MoS 2 (WSe 2 ) vdWHs, as well as the conversion of Schottky contact to ohmic contact from the n-ShC type to p-ShC type. Our results can provide a new approach for the design of future electron nanodevices based on metal/semiconductor TaS 2 /MoS 2 (WSe 2 ) vdWHs.  Interestingly, changes in SBH and contact types can be seen in Figure 9c. When a positive electric field of 0 < E < 0.2 Å is applied, it can be seen that ΦBn > ΦBp. In this case, TaS2/WSe2 vdWHs will form the p-ShC type. Shockingly, when a positive electric field of E ≥ 0.2 Å was applied, the VBM of WSe2 was found to move upward through the Fermi

Computational Methods
Structural optimization and property calculations are performed within the density functional theory framework [54], as implemented in the Vienna ab initio simulation package [55] (VASP), where the ion−electron interaction is implemented by the projectoraugmented plane wave (PAW) approach [56]. The structural models, volumetric data such as electron/nuclear densities, and crystal morphologies are processed by Visualization for Electronic Structural Analysis [57] (VESTA). The electronic exchange-correlation functional is treated using the generalized gradient approximation [58] (GGA) in the form proposed by Perdew, Burke, and Ernzerhof [59] (PBE). The energy cutoff of the plane waves is set to 350 eV, with an energy precision of 10 −6 eV. Atomic positions are fully relaxed until the force on each atom is less than 10 −3 eV/Å. The supercell method is considered to simulate the monolayer, where a vacuum distance of ∼20 Å is used to eliminate the interaction between the adjacent layers. Considering that the GGA usually underestimates the bandgaps, we adopt the Heyd−Scuseria−Ernzerhof (HSE06) hybrid functional [60] to calculate the band structures. The dynamic stabilities and phonon dispersion curves are computed with the supercell approach, as implemented in the Phonopy code [61]. The dipole correction was also included in the calculations.

Conclusions
In summary, we investigated the electronic structure and interfacial properties of metal/semiconductor 1T-TaS 2 /2H-MoS 2 (2H-WSe 2 ) vdWHs by using first-principles calculations. The metallic character of the monolayer 1T-TaS 2 and the intrinsic properties of the monolayer 2H-MoS 2 (2H-WSe 2 ) semiconductor are preserved in TaS 2 /MoS 2 (WSe 2 ) vdWHs. We demonstrate that TaS 2 /MoS 2 and TaS 2 /WSe 2 form n-ShC type and p-ShC type Schottky contacts, with ultralow Schottky barrier heights (SBH) of 0.51 eV and 0.49 eV. The results show that TaS 2 can be considered as an effective metal contact with high charge injection efficiency for MoS 2 , WSe 2 semiconductors. Furthermore, the electronic structure and interfacial properties of TaS 2 /MoS 2 (WSe 2 ) vdWHs are tunable under the action of the strain and electric field, which can not only induce the change in SBH, but also form a transition from the n-ShC type to p-ShC type and from ShC to ohmic contacts. Our findings suggest that metal/semiconductor TaS 2 /MoS 2 (WSe 2 ) vdWHs are promising candidates for optoelectronic devices.